First slide

Accuracy; precision of instruments and errors in measurements

Question

Radius of a wire is 2.50 mm. The length of the wire is 50.0 cm If mass of wire was measured as 25 g, then find the density of wire in correct significant figures. Given, $π = 3.14$ , exact

Moderate

A

$2.2 g / {cm}^{3}$
B

$2.9 g / {cm}^{3}$
C

$2.1 g / {cm}^{3}$
D

$2.5 g / {cm}^{3}$

Solution

Given, r = 2.50 mm
r = 0.250 cm
Further given that,
$l = 50.0 cm$
$m = 25 g$
$π = 3.14$ exact
$ρ = \frac{m}{V} = \frac{m}{π r^{2} l}$
$= \frac{25}{(3.14) (0.250) (0.250) (50.0)}$
$= 2.5477 g / {cm}^{3}$
But in the measured values, least number of significant figures are two. Hence, we will round off the result to two significant figures.
$ρ = 2.5 g / {cm}^{3}$

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